ISSN:
1572-9125
Schlagwort(e):
Differential equations
;
Quadrature method
;
A-stability
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract A class of methods for the numerical solution of systems of ordinary differential equations is given which—for linear systems—gives solutions which conserve the stability property of the differential equation. The methods are of a quadrature type $$y_{i,r} = y_{n,r - 1} + h\sum\limits_{k = 1}^n {a_{ik} f(y_{k,r} ), n = 1,2, \ldots ,n, r = 1,2, \ldots ,} y_{n,0} given$$ wherea ik are quadrature coefficients over the zeros ofP n −P n−1 (v=1) orP n −P n−2 (v=2), whereP n is the Legendre polynomial orthogonal on [0,1] and normalized such thatP m (1)=1. It is shown that $$\left| {y_{n,r} - y(rh) = 0(h^{2n - _v } )} \right|$$ wherey is the solution of $$\frac{{dy}}{{dt}} = f(y), t \mathbin{\lower.3ex\hbox{$\buildrel〉\over{\smash{\scriptstyle=}\vphantom{_x}}$}} 0, y(0) given.$$
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF01946812
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